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arXiv · 1605.00285

The Borell-Ehrhard Game

Ramon van Handel
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Abstract

A precise description of the convexity of Gaussian measures is provided by sharp Brunn-Minkowski type inequalities due to Ehrhard and Borell. We show that these are manifestations of a game-theoretic mechanism: a minimax variational principle for Brownian motion. As an application, we obtain a Gaussian improvement of Barthe's reverse Brascamp-Lieb inequality.

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Ramon van Handel. 2016-05-01. The Borell-Ehrhard Game. https://doi.org/10.1007/s00440-017-0762-4

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